Revisiting the identification problem of a function by the ratio of Laplace transforms of powers

The ratio of Laplace transforms of powers of a function arises in the context of auction theory. The question whether a function is uniquely identified by this ratio has been answered affirmatively, if the function is non-negative, non-decreasing and right analytic.This paper extends the result to a larger class of functions without monotonicity.A conjecture in the literature says that all c\`adl\`ag functions can be identified by the ratio. We disprove this conjecture by providing simple functions that cannot be identified.